Implications of Neutrino Masses on the $K_L\to {\pi }^0\nu \bar{\nu }$ Decay

Abstract

We calculate the different contributions to the decay $K_L\to {\pi }^0\nu \bar{\nu }$ that arise if the neutrinos are massive. In spite of a chiral enhancement factor, we find that these contributions are negligibly small. Compared to the CP violating leading contributions, the CP conserving contributions related to Dirac masses are suppressed by a factor of order $(m_K{m}_{\nu }/m_W^2{)}^2\lesssim 10^{-12}$, and those related to Majorana masses are suppressed by a factor of order $({\alpha }_W{m}_K{m}_s^2{m}_{\nu }/m_W^4{)}^2\lesssim 10^{-29}$. With lepton flavor mixing we find new contributions with a single CP violating coupling leading to a final CP even state or with two CP violating couplings leading to a final CP odd state. These contributions can be of the order of the Standard Model CP conserving contributions to the flavor diagonal modes.

Comments: 14 pages, LaTeX2e; minor corrections and additions, accepted for publication in JHEP